"Perfect Blue" is probably among my Top 10 favorite anime movies. It's a little hard to describe because it's whole mood is to be confusing and evasive - but maybe I can describe it in mish-mash style: a kind of mystery-thriller-horror-surrealist-metaphysical fantasy. Phew!
The movie came out quite a while ago now - 1997. It was directed by Satoshi Kon and written by Sadayuki Murai, based on a novel by Yoshikazu Takeuchi. The plot is about Mima Kirigoe, an ex-Japanese pop idol who left her girl group to become an actress. She becomes a victim of stalking and gets strung along, as does the viewer, in a paranoid head-trip in which she (and you) can't figure out what's real, who is who, and who is a friend or an enemy. It's also a brilliant play on the boundaries of performance, of being the watcher or being watched, and the lines between the personal and the public.
There are some rough scenes from her acting career, but just don't expect to be comfortable, ever. It's a remarkable movie, but it's also a horror-thriller. You're meant to be disoriented and uncomfortable. Okay, that doesn't make it sound appealing - but it really is a super interesting and heart-pounding anime film with shades of Hitchcock, and one that I highly recommend.
I attached a trailer for the movie. It's in Japanese, but the visuals give you a good idea of the mood and aesthetic.

Huh! I'm probably going to take a good look at this. I've been getting more involved in the anime/pop idol world (see: Love Live) so this definitely touches on themes I'll be familiar with. Thanks for the heads up!